What is the fundamental frequency of a guitar string that is 1 m long, the mass per unit length is 50 g/m and the Tension in the string is 50 N.  

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An alternate method is to recognize that for a string fixed at both ends the wavelength is 2 times the length of the string.  In that case you have a wavelength of 2 m.

The relationship between the string tension F(T), the m/L ratio and the velocity of the wave...

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An alternate method is to recognize that for a string fixed at both ends the wavelength is 2 times the length of the string.  In that case you have a wavelength of 2 m.

The relationship between the string tension F(T), the m/L ratio and the velocity of the wave is:  F(T) = m/L * v^2

Solving for the velocity gives 31.62 m/s.

Since v = frequency * wavelength;  31.62 m/s  divided by 2 m = 15.81  Hz as the fundamental frequency.

As you can see, in physics there is often more than one way to end up with the correct answer.

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